The Logical Leap: Induction in Physics

[James Heaps-Nelson]

The problem I have with Harriman is not the lack of mathematics. It is that his model of causality is fundamentally flawed. Physics, at bedrock, is based on a small cluster of conservation laws, which globally cannot be broken. Conservation of energy, conservation of momentum, conservation of angular momentum, conservation of charge and conservation of certain quantities related to weak and strong forces plus gravity. There is no global requirement for entity action causality. That it happens to be true in most cases to a reasonable approximation is of great benefit to us, but it does not fully describe some of the most interesting physical phenomena out there.

I disagree with this. Our knowledge of all causes derives from our knowledge of entities which have certain natures and exhibit certain behaviors. There are no behaviors not of entities of which we know. When you get down to subatomic particles you run up against the Heisenberg uncertainty principle which explains that, since our tools have a necessary limit in their bluntness (Bob will scream Plank length) you cannot measure both the position and velocity of the smallest particles without affecting them. In macroscopic observation, the mass energy of the light that reflects off the moon is insignificant in comparison with the moons mass. It can safely be ignored and we can very accurately measure the moon's position and motion. But with subatomic particles, the mass energy of the photons and the particles involved approach parity and we reach a horizon across which we cannot observe.

This epistemological limit due to the bluntness of our instruments does not amount to a metaphysical claim about the entities at that level. The uncertainty in the measurement is not a lack of identity in the thing. That is the problem with modern philosophical interpretations of subatomic physics. This is not to say that the identity of the thing is not to fluctuate in ways that are not observed at macroscopic levels. That is the problem with some Objectivists' views of physics. The law of identity does not require subatomic particles to behave like discrete billiard balls.

Perhaps we will never achieve the energies necessary to observe the scales we need to reach to get to the next level of understanding. Perhaps we will never have the ability to make the observations needed to posit the entities underlying the phenomena. This does not mean a priori that such entities do not exist. Furthermore, if we were to reach some smaller level underlying the Planck level (I don't imagine we can, but let's posit it) the we would still run up against the uncertainty principle, simply moved down to the next lower level of scale. All knowledge comes at a cost and all effort to achieve it is finite. There will always be horizons and singularities limiting our knowledge. This does not mean that nothing exists beneath those singularities or beyond those horizons.

Ted,

I've always maintained that the strangest, most interesting part of physics is not quantum mechanics or general relativity which are interesting enough, but what actually happens in the standard model. At energies that we know about when we have collisions among particles, the only requirement for the end state is that certain conservation laws are not violated.

Jim

[James Heaps-Nelson]

As a post script to my previous post, there is a particularly interesting field of spectroscopy, called Auger spectroscopy which is based not on the spontaneous emission of quantized light when an electron passes from a higher energy level to a lower energy level in an atom. In the Auger case, it is not a photon which is emitted, but an electron that is created from the energy difference in the transition of a different electron from a higher energy state to a lower energy state.

In a particle accelerator, a number of different outcomes of a collision are possible as long as a small collection of conservation laws are not violated.

Jim

Edited November 28, 2010 by James Heaps-Nelson

[James Heaps-Nelson]

One of the interesting fundamental asymmetries of our universe is the prevalence of matter over antimatter. Particle collisions show that this did not have to be the case as positrons and antiprotons are created as easily in collisions as electrons and protons. A number of interesting medical technologies including positron emission tomography are based on this fact.

Jim

[James Heaps-Nelson]

The problem I have with Harriman is not the lack of mathematics. It is that his model of causality is fundamentally flawed. Physics, at bedrock, is based on a small cluster of conservation laws, which globally cannot be broken. Conservation of energy, conservation of momentum, conservation of angular momentum, conservation of charge and conservation of certain quantities related to weak and strong forces plus gravity. There is no global requirement for entity action causality. That it happens to be true in most cases to a reasonable approximation is of great benefit to us, but it does not fully describe some of the most interesting physical phenomena out there.

I disagree with this. Our knowledge of all causes derives from our knowledge of entities which have certain natures and exhibit certain behaviors. There are no behaviors not of entities of which we know. When you get down to subatomic particles you run up against the Heisenberg uncertainty principle which explains that, since our tools have a necessary limit in their bluntness (Bob will scream Plank length) you cannot measure both the position and velocity of the smallest particles without affecting them. In macroscopic observation, the mass energy of the light that reflects off the moon is insignificant in comparison with the moons mass. It can safely be ignored and we can very accurately measure the moon's position and motion. But with subatomic particles, the mass energy of the photons and the particles involved approach parity and we reach a horizon across which we cannot observe.

This epistemological limit due to the bluntness of our instruments does not amount to a metaphysical claim about the entities at that level. The uncertainty in the measurement is not a lack of identity in the thing. That is the problem with modern philosophical interpretations of subatomic physics. This is not to say that the identity of the thing is not to fluctuate in ways that are not observed at macroscopic levels. That is the problem with some Objectivists' views of physics. The law of identity does not require subatomic particles to behave like discrete billiard balls.

Perhaps we will never achieve the energies necessary to observe the scales we need to reach to get to the next level of understanding. Perhaps we will never have the ability to make the observations needed to posit the entities underlying the phenomena. This does not mean a priori that such entities do not exist. Furthermore, if we were to reach some smaller level underlying the Planck level (I don't imagine we can, but let's posit it) the we would still run up against the uncertainty principle, simply moved down to the next lower level of scale. All knowledge comes at a cost and all effort to achieve it is finite. There will always be horizons and singularities limiting our knowledge. This does not mean that nothing exists beneath those singularities or beyond those horizons.

Ted,

You make a persuasive case, but when would you concede that the universe in certain cases, does not have more secrets to yield, that things just act too strangely for our imagination? Why does one 100 GeV particle have a weak nuclear interaction and another simply give off more energy as a lower energy photon and itself become a lower energy photon? At 100 GeV, a photon probably acts identically to a W or Z boson. A good part of the reason our universe is the way it is lies in this symmetry-breaking.

There is no lower scale, only different fundamental particles at higher energies. The word particle is fuzzy too. You could call each higher level at which symmetry-breaking occurs an "energy resonance". The real unknown is where these energy resonances occur. That is the real frontier in particle physics: at higher and higher energies.

Jim

Edited November 28, 2010 by James Heaps-Nelson

[Dennis Hardin]

The problem I have with Harriman is not the lack of mathematics. It is that his model of causality is fundamentally flawed. Physics, at bedrock, is based on a small cluster of conservation laws, which globally cannot be broken. Conservation of energy, conservation of momentum, conservation of angular momentum, conservation of charge and conservation of certain quantities related to weak and strong forces plus gravity. There is no global requirement for entity action causality. That it happens to be true in most cases to a reasonable approximation is of great benefit to us, but it does not fully describe some of the most interesting physical phenomena out there.

Jim,

I'm a little astonished that you would say that "there is no global requirement for entity action causality." What other kind of causality is there? Actions without entities that act? The whole purpose of axioms is to set certain ground rules for all further scientific inquiry. If you toss out causality, you toss out identity (since the capacity for a range of action is necessarily limited by a thing's nature). And since such axioms are subsumed by all knowledge, you effectively invalidate all human knowledge.

Incidentally, the error of the Heisenberg uncertainty principle is the notion that certain things are, in principle, unknowable, as opposed to simply unknown (due to deficiencies with present methods of measurement). That is a Kantian premise, and absolutely without foundation. It would require some sort of mystical celestial omniscience to "know" that certain things cannot be known.

[Xray]

I aim to examine every word written in the book. To the last jot and tittle. The book will be analyzed precisely on the basis of its contents -as written-, not as possible intended. I don't do intentions. I do not look between the lines. I do literal reading. I am willing to bet Harriman has never been reviewed by an Aspie.

What precisely do you mean by "I do literal reading"? I suppose when you read e. g. the sentence "That's a pretty kettle of fish", you will know that it is not about actual fish but about something else, so you would not be doing literal reading.

Anyway the book is on the way and I shall read it carefully when I get it.

My feeling is you are going to have field day reviewing it ...

As would Dragonfly, if he were still posting here. DF's leaving is a big loss for this forum.

In the book will find statements like :

"The central issue here is the failure of philosophers to offer a solution for what has been called the the problem of induction." (D. Harriman, TLL, p. 6)

Looks like Harriman believes he can solve it, for he says on the next page: "What is the method of valid induction that can prove the generalization to which it leads?" (DH)

How is Harriman going to prove a generalization reached by induction?

There are some here who are physics experts and some who are not physics experts but who can follow physics mathematically if it is well explained. A board with Dragonfly, Dan Ust, Ellen Stuttle, Stephen Boydstun and others, is the perfect place for Baal's approach.

Jim,

Dan Ust and Dragonfly no longer post here.

I think even Objectivists will miss DF's outstanding contributions to this forum.

Edited November 28, 2010 by Xray

[BaalChatzaf]

What precisely do you mean by "I do literal reading"? I suppose when you read e. g. the sentence "That's a pretty kettle of fish", you will know that it is not about actual fish but about something else, so you would not be doing literal reading.

There is where you are wrong.

My first inclination is to seek the kettle of fish in the context. Failing to find it, I will conclude that the phrase in the sentence was idiomatic and I will search my mental idiom data base for a probable meaning. My inclination is to be literal in my reading and over the years it has also become my preference. When I do use puns in my speech and writing I often mark them carefully as puns so no one else will be confused.

If the context of the sentence contains fish or kettles thereof how should I have read the sentence?

How would you read it?

My literalness, at times, causes social awkwardness (for me). So when I am among people who I care for I have to consciously suppress my literalness. That is one of the prices I pay for getting along with the NTs. But as the old proverb goes --- when in Rome... . It is true even when I am not in Rome. When in Monroe Township do as the Monrovians do.

Ba'al Chatzaf

Edited November 28, 2010 by BaalChatzaf

[James Heaps-Nelson]

The problem I have with Harriman is not the lack of mathematics. It is that his model of causality is fundamentally flawed. Physics, at bedrock, is based on a small cluster of conservation laws, which globally cannot be broken. Conservation of energy, conservation of momentum, conservation of angular momentum, conservation of charge and conservation of certain quantities related to weak and strong forces plus gravity. There is no global requirement for entity action causality. That it happens to be true in most cases to a reasonable approximation is of great benefit to us, but it does not fully describe some of the most interesting physical phenomena out there.

Jim,

I'm a little astonished that you would say that "there is no global requirement for entity action causality." What other kind of causality is there? Actions without entities that act? The whole purpose of axioms is to set certain ground rules for all further scientific inquiry. If you toss out causality, you toss out identity (since the capacity for a range of action is necessarily limited by a thing's nature). And since such axioms are subsumed by all knowledge, you effectively invalidate all human knowledge.

Incidentally, the error of the Heisenberg uncertainty principle is the notion that certain things are, in principle, unknowable, as opposed to simply unknown (due to deficiencies with present methods of measurement). That is a Kantian premise, and absolutely without foundation. It would require some sort of mystical celestial omniscience to "know" that certain things cannot be known.

Dennis,

I'm perfectly OK with entity action causality as a bookkeeping entry and how it's used philosophically outside a physics context. It is much, much better than Humean event driven causality.

There are several problems and assumptions for using it in a physics context for subatomic particles. I will list only a few to avoid being tedious:

1. You are assuming that a particle is an entity that is "separable" causally from the space surrounding it.

2. The term particle connotes things which import a Newtonian context such as fixed mass, energy etc. or even a fixed character as a certain kind of particle. Probably the term energy resonance is better for subatomic "particles". What happens when physicists add energy to a particle in a particle accelerator is that it becomes a very different "entity". To use the example I gave above, something very strange happens at 100 GeV to accelerated charged particles. The electric and weak nuclear force become unified and are the same force. Probably what happens is that a 100 GeV photon (which mediates the electric force) acts very much similar to a 100GeV W or Z boson that mediates the weak nuclear force.

I'm OK with using the term entity when it's used for things just above the atomic scale because it denote something that has fixed attributes upon which "causal bookkeeping" can be performed. Physicists do bookkeeping on conservation laws because they represent quantities which remain the same globally before and after a subatomic interaction.

Incidentally, I don't think the foregoing presents any particular problem, except for philosophers that want to read something mystical or skeptical into contexts that are very difficult and counterintuitive conceptually.

Jim

Edited November 28, 2010 by James Heaps-Nelson

[BaalChatzaf]

I'm OK with using the term entity when it's used for things just above the atomic scale because it denote something that has fixed attributes upon which "causal bookkeeping" can be performed. Physicists do bookkeeping on conservation laws because they represent quantities which remain the same globally before and after a subatomic interaction.

Incidentally, I don't think the foregoing presents any particular problem, except for philosophers that want to read something mystical or skeptical into contexts that are very difficult and counterintuitive conceptually.

Jim

You have adumbrated the spirit of the "least action" principle and the preservation (invariance) of the Lagrangians (and other action functionals) under transformation. This is the center of Noether's theorem which ties together conservation and invariance under group transformations. This is a very rarified and abstract notion of causality but it has turned out to be the most fruitful approach taken by physicists.

This trend in physics started way back in the day of Lagrange, D'Lambert, Benoulli, Hamilton and others.

Ba'al Chatzaf

[James Heaps-Nelson]

I'm OK with using the term entity when it's used for things just above the atomic scale because it denote something that has fixed attributes upon which "causal bookkeeping" can be performed. Physicists do bookkeeping on conservation laws because they represent quantities which remain the same globally before and after a subatomic interaction.

Incidentally, I don't think the foregoing presents any particular problem, except for philosophers that want to read something mystical or skeptical into contexts that are very difficult and counterintuitive conceptually.

Jim

You have adumbrated the spirit of the "least action" principle and the preservation (invariance) of the Lagrangians (and other action functionals) under transformation. This is the center of Noether's theorem which ties together conservation and invariance under group transformations. This is a very rarified and abstract notion of causality but it has turned out to be the most fruitful approach taken by physicists.

This trend in physics started way back in the day of Lagrange, D'Lambert, Benoulli, Hamilton and others.

Ba'al Chatzaf

You're right, Bob. I went as far as I could go in the explanation without the math. Thanks for stating it in a more exact and technically correct way. Hopefully my explanation will pass muster with Phil :-).

Jim

Edited November 28, 2010 by James Heaps-Nelson

[James Heaps-Nelson]

By the way, if anyone with a basic calculus background wants to see a cool explanation of what Bob is talking about, check this out from John Baez:

http://math.ucr.edu/home/baez/noether.html

Jim

[BaalChatzaf]

How is Harriman going to prove a generalization reached by induction?

.

He isn't. There are already cases of generalizing inductions starting from a finite set of true instances and leading to a general conclusion which is false.

-(x)P(x) == Ex[-P(x)]

Ba'al Chatzaf

[George H. Smith]

I think even Objectivists will miss DF's outstanding contributions to this forum.

Absolutely. I miss DF's secret credentials, his incessant appeals to authority in matters of philosophy, and his contempt for everything having to do with Objectivism. What shall we do without him?

Ghs

[George H. Smith]

How is Harriman going to prove a generalization reached by induction?

.

He isn't. There are already cases of generalizing inductions starting from a finite set of true instances and leading to a general conclusion which is false.

-(x)P(x) == Ex[-P(x)]

Ba'al Chatzaf

The symbolic expression of this truism makes it look oh-so-much more impressive.

Ghs

[BaalChatzaf]

The symbolic expression of this truism makes it look oh-so-much more impressive.

Ghs

Impressive does not count. Being correct and complete does. I am a stickler for correct and complete (when practical).

Do you have a substantial objection to what I wrote? If so, please let is see it.

Ba'al Chatzaf

[BaalChatzaf]

The symbolic expression of this truism makes it look oh-so-much more impressive.

Ghs

One man's truism and another man's tautology. A tautological formula is one that is true under all mappings of the predicates and individual variables. In short, a formula that is (proverbially) as good as gold. All of logic is based on tautologies, or as you say, truisms.

Ba'al Chatzaf

[George H. Smith]

The symbolic expression of this truism makes it look oh-so-much more impressive.

Ghs

Impressive does not count. Being correct and complete does. I am a stickler for correct and complete (when practical).

Do you have a substantial objection to what I wrote? If so, please let is see it.

Ba'al Chatzaf

I have no objection to the claim that induction is a fallible method of reasoning. That's all you really said, and this common philosophical observation -- one that even Harriman doesn't deny -- does not become more "correct and complete" by being expressed in an artificial language.

Ghs

[merjet]

There are already cases of generalizing inductions starting from a finite set of true instances and leading to a general conclusion which is false.

-(x)P(x) == Ex[-P(x)]

Ba'al Chatzaf

Some does not imply all. Or are you trying to claim it does?

[BaalChatzaf]

The symbolic expression of this truism makes it look oh-so-much more impressive.

Ghs

Impressive does not count. Being correct and complete does. I am a stickler for correct and complete (when practical).

Do you have a substantial objection to what I wrote? If so, please let is see it.

Ba'al Chatzaf

I have no objection to the claim that induction is a fallible method of reasoning. That's all you really said, and this common philosophical observation -- one that even Harriman doesn't deny -- does not become more "correct and complete" by being expressed in an artificial language.

Ghs

In a way, yes. One takes away all the connotative baggage of natural language.

And besides, symbols use less ink and fewer strokes.

Apparently the manifestly true statement: induction is NOT a valid mode of inference has to be repeated and repeated because many still do not get it.

Induction is part of discovery, not part of justification.

Ba'al Chatzaf

[kiaer.ts]

There are several problems and assumptions for using it in a physics context for subatomic particles. I will list only a few to avoid being tedious:

1. You are assuming that a particle is an entity that is "separable" causally from the space surrounding it.

2. The term particle connotes things which import a Newtonian context such as fixed mass, energy etc. or even a fixed character as a certain kind of particle. Probably the term energy resonance is better for subatomic "particles". What happens when physicists add energy to a particle in a particle accelerator is that it becomes a very different "entity".

These are possible but not necessary misconceptions, and I see no hint of them in what Dennis wrote above. Indeed, Rand dealt with such mistakes in her treatment of the Frozen Concept. Entity doesn't mean unchangeable existent. The hylomorphic Objectivist metaphysics deals with such change. An acorn is no less an entity because it changes into an oak. If it is the nature of a particle to decay by emitting photon and other particles, then that is its nature as an entity.

[BaalChatzaf]

There are already cases of generalizing inductions starting from a finite set of true instances and leading to a general conclusion which is false.

-(x)P(x) == Ex[-P(x)]

Ba'al Chatzaf

Some does not imply all. Or are you trying to claim it does?

I am stating a theorem in first order predicate logic.

In plain language the one negates a general statement is to instantiate its negative. One counterexample is sufficient to bust a general statement. Have you ever heard the old chestnut ("chestnut" used metaphorically here) the exception PROVES the rule. The correct meaning is that the exception TESTS the rule. One exception and the rule is false.

Ba'al Chatzaf

[George H. Smith]

Apparently the manifestly true statement: iinduction is NOT a valid mode of inference has to be repeated and repeated because many still do not get it.

Induction is part of discovery, not part of justification.

Ba'al Chatzaf

If by "valid," you mean "deductively valid," then it is true by definition that induction is not a valid method of reasoning. Induction is not deduction. BFD.

But if we construe "valid" in a more general sense to mean a process of reasoning that can generate authentic knowledge, then induction is a valid mode of inference. We use it all the time with reliable results.

Moreover, if induction is "part of discovery," then how can a supposedly invalid mode of inference discover anything? Why not consult a psychic or gaze into crystal ball instead?

Ghs

[George H. Smith]

There are already cases of generalizing inductions starting from a finite set of true instances and leading to a general conclusion which is false.

-(x)P(x) == Ex[-P(x)]

Ba'al Chatzaf

Some does not imply all. Or are you trying to claim it does?

I am stating a theorem in first order predicate logic.

In plain language the one negates a general statement is to instantiate its negative. One counterexample is sufficient to bust a general statement. Have you ever heard the old chestnut ("chestnut" used metaphorically here) the exception PROVES the rule. The correct meaning is that the exception TESTS the rule. One exception and the rule is false.

Ba'al Chatzaf

I am familiar with symbolic logic, and I also know that we don't need symbolic logic to tell us that one counterexample can disprove a general rule. Aristotelian logicians were discussing examples like "All swans are white" centuries before Russell and Whitehead happened along.

The problem with your formulation is that it does not clearly specify the inductive "rule" that is supposedly falsified. So what inductive "rule" would that be? Try stating it in plain English.

Ghs

[James Heaps-Nelson]

The problem I have with Harriman is not the lack of mathematics. It is that his model of causality is fundamentally flawed. Physics, at bedrock, is based on a small cluster of conservation laws, which globally cannot be broken. Conservation of energy, conservation of momentum, conservation of angular momentum, conservation of charge and conservation of certain quantities related to weak and strong forces plus gravity. There is no global requirement for entity action causality. That it happens to be true in most cases to a reasonable approximation is of great benefit to us, but it does not fully describe some of the most interesting physical phenomena out there.

Jim,

I'm a little astonished that you would say that "there is no global requirement for entity action causality." What other kind of causality is there? Actions without entities that act? The whole purpose of axioms is to set certain ground rules for all further scientific inquiry. If you toss out causality, you toss out identity (since the capacity for a range of action is necessarily limited by a thing's nature). And since such axioms are subsumed by all knowledge, you effectively invalidate all human knowledge.

Incidentally, the error of the Heisenberg uncertainty principle is the notion that certain things are, in principle, unknowable, as opposed to simply unknown (due to deficiencies with present methods of measurement). That is a Kantian premise, and absolutely without foundation. It would require some sort of mystical celestial omniscience to "know" that certain things cannot be known.

Dennis,

I'm also going to make an attempt at what I'm trying to say and maybe it will be a better explanation. It is not that quantum mechanics is unknowable. It is that it is fundamentally statistical and discontinuous with respect that certain attributes or combinations of attributes that human beings care about. The statistical nature of quantum mechanics is quite regular, predictable and reasonable to handle in the aggregate and scientists and engineers do it all the time because the statistics follows a normal distribution. It is not that the properties of quantum behavior are not knowable, it is that attributes that we are familiar with on the macro level do not exist in continuous and nonstatistical quantities at the subatomic level.

Now there is chaotic behavior that is unpredictable. It is knowable to a very tight precision at any given point in time. Imagine that you are taking an infinite sum of the digits of a nonrepeating irrational (not expressable as a fraction) number like pi. There are mathematical procedures for generating the series, but someone says predict the sum after the 3070th digit before computing the series. Is it unknowable? No. But it is unpredictable, until you sum the series.

How do scientists and engineers handle chaotic behavior. By taking repeated measurements of the quantities they care about in real time and making predictions about small intervals of time later. This is much more difficult than quantum behavior and at some finite, sometimes small period of time later, we cannot predict what the behavior will be.

Jim

Edited November 28, 2010 by James Heaps-Nelson

[James Heaps-Nelson]

There are several problems and assumptions for using it in a physics context for subatomic particles. I will list only a few to avoid being tedious:

1. You are assuming that a particle is an entity that is "separable" causally from the space surrounding it.

2. The term particle connotes things which import a Newtonian context such as fixed mass, energy etc. or even a fixed character as a certain kind of particle. Probably the term energy resonance is better for subatomic "particles". What happens when physicists add energy to a particle in a particle accelerator is that it becomes a very different "entity".

These are possible but not necessary misconceptions, and I see no hint of them in what Dennis wrote above. Indeed, Rand dealt with such mistakes in her treatment of the Frozen Concept. Entity doesn't mean unchangeable existent. The hylomorphic Objectivist metaphysics deals with such change. An acorn is no less an entity because it changes into an oak. If it is the nature of a particle to decay by emitting photon and other particles, then that is its nature as an entity.

Ted, sure. I don't see any problem with quantum behavior or other unpredictable phenomena with regard to Rand's identity-based metaphysics. What is a problem is when certain a priori preconceptions of what an entity can or cannot be or can or cannot do are made without making observations.

Take the example of what happens in muon catalyzed nuclear fusion. One method of getting two heavy hydrogen atoms to fuse is to chemically bond them with a muon which has a much bigger rest mass than an electron. Now the interesting part is that without quantum behavior, the two hydrogen atoms would be too far away from each other to fuse via the strong nuclear force, but they do anyway because of quantum tunneling.

Jim

Edited November 28, 2010 by James Heaps-Nelson